These default you have, all have texture files in them that replaces the original right? I would export those eye textures, then use them to make new non default eyes.
I never made eyes, but this is how I would do it.

As long as the textures for dogs/cats are different in the file, you can probably delete the ones you don't want from the default file.

This creator made non-default eyes for pets, and has made a tutorial on how to do it yourself: http://kitteninthewindow.tumblr.com...ime-has-finally
You should be able to extract textures from default eyes you like, and make new custom ones with the method int he tutorial.